Calculating Mass of a Structural I-beam

[MattWakes]

Homework Statement

A structural I-beam is made of steel. L = 12.1 cm, H = 32.0 cm and the width of the beam is W = 1.11 cm. What is the mass of a section 1.75 m long? The density of steel is 7.56E+3 kg/m3.

Homework Equations

d=m/v

The Attempt at a Solution

I can't copy the image of the i-beam here.. but, as you might expect, it resembles an i. I found the volume of the total beam, and subtracted from it the volume of the missing section. Then I converted cubic cm to cubic metres and multiplied by the density of steel. Then I found the ratio of length 1.75m to 12.1 cm and multiplied that by my newfound mass.. something is wrong, though.

mass= (7.56e3kg/m^3)((12.1*1.11*32.0-10.99*1.11*29.78)cm^3)(10^-2m/cm)^3/(0.121m)=7.275 kg. Thanks in advance.

 

[SteamKing]

If you can't copy the image, try to describe the section.

1. What is the depth of the beam, from top of the top flange to the bottom of the bottom flange?
2. What is the width of the flange?
3. What is the thickness of the flange?
4. What is the thickness of the web (the bit connecting the two flanges)?

OTOH, if you calculate the cross sectional area of the beam, then the volume will be L*Area, and from this you can find the mass of the beam.

 

[MattWakes]

The flange and web are unknown to me. How do I calculate the cross sectional area of the beam?

 

[SteamKing]

If the flange and web are unknown, how do you expect to calculate the mass of the beam? The dimensions given in the OP must refer to some of the features of the beam.

 

[Nickie]

I would like to first commend you for your attempt at finding the mass of the structural I-beam. However, there are a few issues with your solution that may have led to the incorrect result.

Firstly, when calculating the volume of the total beam, you have not taken into account the thickness of the beam. The width of the beam given in the homework statement is 1.11 cm, which means the thickness of the beam is also 1.11 cm. Therefore, the volume of the total beam should be (12.1*1.11*32.0) cm^3.

Secondly, when finding the volume of the missing section, the dimensions should be (10.99*1.11*29.78) cm^3, as this is the missing section of the beam.

Lastly, when finding the mass, you have divided by 0.121m instead of 1.75m. This is why your answer is much smaller than expected. The correct calculation would be:

mass = (7.56e3 kg/m^3) * [(12.1*1.11*32.0) cm^3 - (10.99*1.11*29.78) cm^3] * (1.75 m / 100 cm)^3 = 118.6 kg

I hope this helps you understand where you may have gone wrong and how to correctly calculate the mass of the structural I-beam. Keep up the good work in your scientific pursuits!